A. Field of the Invention
The present invention relates to manipulating pulses of electromagnetic energy transmitted in a dispersive medium (e.g., waveguides, free space, etc.) having a dispersive characteristic and, in particular, to apparatus, systems, and methods of compensating for the dispersion. One relevant application is dispersion management or compensation in fiber optics in communications systems but the present invention is not so limited.
B. Problems in the State of the Art Dispersion management is an indispensable element of optical communication systems, where dispersive effects—originating from the materials, waveguide (fiber) geometries, and optical amplification—accumulate to set limits on both the distance and the bit rate of the data transfer. Various compensation schemes have been developed to manage group velocity dispersive effects (see, for example, [1] G. P. Agrawal, Fiber-Optic Communication Systems, Wiley Series in Microwave and Optical Engineering (Wiley, New York, 2010); and [2] S. Ramachandran, Fiber Based Dispersion Compensation, Optical and Fiber Communications Reports Vol. 5 (Springer, New York, 2007)), but fundamental limits on integrability, footprint, and customizability are imposed by the physics in contemporary dispersion management systems. Although not necessarily apparent to one skilled in the art without having the benefit of this disclosure, recent advances in nanofabrication and breakthroughs in the field of metamaterials have opened up a new range of possibilities in device development. See, for example, [3] D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, Science 305, 788 (2004); [4] R. Engheta and R. W. Ziolkowski, Metamaterials, Physics and Engineering Explorations (Wiley-IEEE, New York, 2006); [5] V. M. Shalaev, Nat. Photon. 1, 41(2007); [6] Y. Liu and X. Zhang, Chem. Soc. Rev. 40, 2494 (2011); [7] C. M. Soukoulis and M. Wegener, Nat. Photon. 5, 523 (2011); [8] N. I. Zheludev and Y. S. Kivshar, Nat. Mater. 11, 917 (2012); all incorporated by reference herein.
Most metamaterials rely on highly resonant structures that force light to undergo a large phase change near resonance frequencies. This results in strong dispersion in a narrow spectral range, making them suitable for dispersion management purposes. Indeed, it was recently shown that light passing through a so-called metasurface experiences up to a 2 π phase shift upon transmission/reflection in a system that is much thinner than the free-space wavelength of the incident light, mimicking a phase discontinuity. See, for example, [9] N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, Science 334, 333 (2011); [10] F. Aieta, P. Genevet, M. a. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Capasso, Nano Lett. 12, 4932 (2012); both incorporated by reference herein. Phase properties in such metasurfaces are shown to be easily tailorable, although it is important to note that this comes at the cost of absorption in the dispersive region. See, for example, B. Dastmalchi, P. Tassin, T. Koschny, and C. M. Soukoulis, Strong group-velocity dispersion compensation with phase-engineered sheet metamaterials, PHYSICAL REVIEW B 89, 115123 (2014), incorporated by reference herein.
Thus, as can be appreciated by those skilled in the art, a number of factors come into play regarding solutions for this type of dispersion. As can be appreciated by the discussion earlier, dispersion shifted fibers literally require specific long (e.g. kilometer (km) scale), spliced lengths added along the transmission path. Therefore, if a primary concern is the space occupied by the compensating device, they are counter-indicated as a solution. Their form factors are large. On the other hand, if size is not the primary concern and bandwidth is, dispersion shifted fibers can support very broad bandwidth.
Over and above signal loss, Bragg gratings must be manufactured to quite exacting standards. Therefore, unless the system does not have to meet severely exacting fabrication tolerances, Bragg gratings might be counter-indicated as a solution.
The above-discussed considerations or factors, as well as others, must be balanced. They can be antagonistic relative to one another. For example, an ideal dispersion compensation device might have the following types of characteristics: (a) large negative dispersion coefficient, (b) low attenuation, (c) minimal nonlinear contributions, (d) wide bandwidth, (e) also corrects dispersion slope, (f) causes minimal ripple, (g) is polarization independent, (h) has a size and form factor much smaller than the optical fiber it is compensating, (i) is adaptable to a relatively wide variety of applications, and (j) is relatively efficiently and economically manufacturable. Another factor is absorption. Some materials have higher absorption rates than others. Some materials cannot support strong dispersion in highly localized volumes of space. Thus, there are both operational and practical considerations.
Therefore, room for improvement exists in the technical field of optical fiber communications. Improvement to the dispersion problem may be applied in other applications and contexts. The invention may possibly be applied beyond fiber optic transmissions, at least in applications at sufficiently high frequencies where it makes practical sense. This can include but is not limited to wires (e.g. in high speed electronics and electronics interconnects), transmission lines, microwave transmission, and perhaps even free space transmissions.